The excitation of a parallel-plate electromagnetic pulse (EMP) simulator by an electromagnetic pulse via a conical transmission line is analyzed. The analysis first establishes an exact formulation of the problem by use of the technique of electric-field integrodifferential equations. It then goes over to a simpler, approximate formulation in the form of an integrodifferential equation for the total longitudinal surface current flowing on the simulator. This equation is further transformed into an integral equation, and the model structure of its solution investigated. A self-consistent method for solving the integral equation is developed. An analytical formula for the current in the transverse-electromagnetic (TEM) mode is thereby obtained. The analysis concludes with a numerical study of the TEM current and its variation with the parameters of the simulator geometry.